$J$ is the midpoint of $\overline{CT}$ C J T If: $ CJ = 8x + 2$ and $ JT = 7x + 6$ Find $CT$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {8x + 2} = {7x + 6}$ Solve for $x$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 8({4}) + 2$ $ JT = 7({4}) + 6$ $ CJ = 32 + 2$ $ JT = 28 + 6$ $ CJ = 34$ $ JT = 34$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {34} + {34}$ $ CT = 68$